Abstract
A disk graph is the intersection graph of a set of disks in the plane. For a k-tuple ( p 1 , … , p k ) of positive integers, a distance constrained labeling of a graph G is an assignment of labels to the vertices of G such that the labels of any pair of vertices at graph distance i in G differ by at least p i , for i = 1 , … , k . In the case when k = 1 and p 1 = 1 , this gives a traditional coloring of G. We propose and analyze several online and offline labeling algorithms for the class of disk graphs.
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